Feature aggregation in GAT applies the normalized attention coefficient to compute a linear combination of neighbor's features as \(\mathbf {X}_{agg, i}=\sum _{j\in \mathcal {N}(i)}\alpha _{ij}\mathbf {X}_{trans, j}\) , where \(\alpha _{ij}=softmax_j(e_{ij})\) , \(e_{ij}=\text{LeakyReLU}(\mathbf {X}_{trans, i}^{\top }\mathbf {w}_i+\mathbf {X}_{trans, j}^{\top }\mathbf {w}_j)\) , and \(\mathbf {w}_i\)  and \(\mathbf {w}_j\)  are learnable column vectors. Prior study [1]} demonstrates that one-step gradient descent with adaptive stepsize \(\frac{1}{\sum _{j\in \tilde{\mathcal {N}}(i)}(c_i+c_j)}\)  for the following objective problem:
\(\min \limits _{\mathbf {F}}\sum _{i\in \mathcal {V}}||\mathbf {F}_i-\mathbf {X}_{trans, i}||^2_F + \frac{1}{2}\sum _{i\in \mathcal {V}}c_i\sum _{j\in \tilde{\mathcal {N}}(i)}||\mathbf {F}_i-\mathbf {F}_j||_F^2. \nonumber \) 
